The interval order polytope of a digraph
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We introduce the interval order polytope of a digraph D as the convex hull of interval order inducing arc subsets of D. Two general schemes for producing valid inequalities are presented. These schemes have been used implicitly for several polytopes and they are applied here to the interval order polytope. It is shown that almost all known classes of valid inequalities of the linear ordering polytope can be explained by the two classes derived from these schemes. We provide two applications of the interval order polytope to combinatorial optimization problems for which to our knowledge no polyhedral descriptions have been given so far. One of them is related to analyzing DNA subsequences.
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- The interval order polytope of a digraph
- Book Title
- Integer Programming and Combinatorial Optimization
- Book Subtitle
- 4th International IPCO Conference Copenhagen, Denmark, May 29–31, 1995 Proceedings
- pp 50-64
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- Lecture Notes in Computer Science
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- Springer Berlin Heidelberg
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- 1. Institut für Wirtschaftsinformatik, Humboldt-Universität zu Berlin, Spandauer Straße 1, D-10178, Berlin, Germany
- 2. Fachbereich Mathematik (MA 6-1), Technische Universität Berlin, Straße des 17. Juni 136, D-10623, Berlin, Germany
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